Back Original

Computers and Automata (1953)

What is the paper before this!? It looks interesting as well!

Samuel Butler was a 19th century English novelist, essayist and cri...

The estimation of energy consumption in the human brain is usually ...

## Jacquard Loom During the 1700s, a number of French weavers de...

For the sake of comparison about where we stand today: - Estimate ...

The all-or-none principle states that if a single neuron is stimula...

"Audrey" (Automatic Digit Recognition Unit) was a very early speec...

At the time of publishing of Shannon's paper it had only been 16 ye...

A traditional, or "deterministic" Turing machine, as described by A...

This is known as the halting problem. The halting problem is the pr...

Shannon is likely alluding to the following quote: > Everybody ta...

Hex is a strategy game played on a hexagonal grid. The goal is to c...

Nim is a strategic mathematical game where two players take turns r...

Checkers was one of the first non trivial games where machines were...

Shannon made significant contributions to the field of chess progra...

![](https://i.imgur.com/y7GligR.jpg) *Claude Shannon and the These...

![](https://cdn.technologyreview.com/i/images/128024.jpg?sw=700&cx=...

PROCEEDINGS

OF

THE

I.R.E.

It

will

be

seen

that

the

effect

of

expressing

approval

when

a

particular

figure

has

been

printed

is

to

increase

the

chance

of

that

figure

being

printed

on

subsequent

occasions,

and

so,

if

done

sufficient

times,

to

give

the

appearance

of

a

conditioned

reflex

action

having

been

established.

GENERALIZED

LEARNING

PROGRAMS

The

construction

of

a

learning

program

of

the

above

type

presents

no

difficulty

to

anyone

who

is

familiar

with

the

technique

of

programming.

However,

such

a

pro-

gram

makes

it

possible

to

teach

the

machine

only

those

things

which

the

programmer

had

in

mind

when

he

wrote

the

program.

For

example,

the

program

just

described

would

not

enable

the

operator

to

teach

the

machine

to

print

different

figures

after

alternate

stimuli.

If

the

pro-

grammer

had

wished

to

do

so,

he

could

have

allowed

for

this

possibility

in his

program.

In

fact,

at

the

expense

of

making

the

program

longer

and

more

complicated,

he

could

include

any

number

of

extra

features,

but

obvi-

ously

he

could

not

think

of

every

possible

experiment

which

anyone

might

wish

to

try

on

the

machine.

All

the

programmer

is

doing,

in

fact,

is

to

program

the

action

of

the

machine

as

it

were

at

one

remove;

when

he

writes

the

program

he

visualizes,

if

not

in

complete

de-

tail,

at

any

rate

in

general

terms,

all

the

possible

actions

which

the

machine

can

take

in

response

to

legitimate

ac-

tions

on

the

part

of

the

operator.

Such

programms

are

not,

therefore,

as

interesting

as

at

first

sight

might

appear

from

the

point

of

view

of

this

article.

What

is

wanted

is

a

"generalized"

learning

pro-

gram,

which

would

enable

an

operator

to

teach

the

ma-

chine

anything

he

chose,

whether

the

idea

of

his

doing

so

had

occurred

to

the

programmer

or

not.

I

believe

that

such

a

program

would

not

be

a

mere

elaboration

of

the

simple

learning

programs

which

have

been

constructed

up

to

date

but

would

need

to

be

based

on

some

entirely

new

ideas.

Presumably

the

program

would

modify

and

extend

itself

as

the

learning

process

went

on.

As

I

have

pointed

out,

existing

machines

contain

the

means

for

this

extension;

the

difficulty

is

to

construct

a

program

to

make

use

of

them.

If

such

a

program

could

be

made

then

it

would

be

possible

to

teach

the

machine

in

much

the

same

way

as

a

child

is

taught.

Whether

the

new

ideas

I

have

referred

to

will

be

forth-

coming,

it is

hard

to

say.

Certainly,

for

the

present,

progress

appears

to

be

held

up.

Perhaps

this

will

give

comfort

to

those

who

cannot

bear

the

idea

of

machines

thinking;

on

the

other

hand

it

may

stimulate

others

to

further

effort.

BIBLIOGRAPHY

E.

C.

Berkeley,

"Giant

Brains,"

John

Wiley

&

Sons,

New

York,

N.

Y.;

1949.

A.

G.

Oettinger,

"Programming

a

digital

computer

to

learn,"

Phil.

Mag.,

vol.

7,

no.

43,

pp.

1243-1263;

1952.

C.

E.

Shannon,

"Programming

a

computer

for

playing

chess,"

Ibid.,

vol.

7,

no.

41,

pp.

256-275;

1950.

A.

M.

Turing,

"Computing

machinery

and

intelligence,"

Mind,

vol.

59,

pp.

433-460;

1950.

M.

V.

Wilkes,

"Can

machines

think?"

The

Spectator,

no.

6424,

pp.

177-178;

1951.

"Automatic

calculating

machines,"

Jour.

Roy.

Soc.

A.,

vol.

100,

pp.

56-90;

1951.

M.

V.

Wilkes,

D.

J.

Wheeler,

and

S.

Gill,

"The

Preparation

of

Pro-

grams

for

an

Electronic

Digital

Computer,"

Addison-Wesley

Cambridge,

Mass.;

1951.

Computers

and

Automata*

CLAUDE

E.

SHANNONt,

FELLOW,

IRE

Summary-This

paper

reviews

briefly

some

of

the

recent

de-

velopments

in

the

field

of

automata

and

nonnumerical

computation.

A

number

of

typical

machines

are

described,

including

logic

ma-

chines,

game-playing

machines

and

learning

machines.

Some

theo-

retical

questions

and

developments

are

discussed,

such

as

a

com-

parison

of

computers

and

the

brain,

Turing's

formulation

of

comput-

ing

machines

and

von

Neumann's

models

of

self-reproducing

ma-

chines.

*

Decimal

classification:

621.385.2.

Original

manuscript

received

by

the

Institute,

July

17,

1953.

t

Bell

Telephone

Laboratories,

Murray

Hill,

N.

J.

INTRODUCTION

SOAMUEL

BUTLER,

in

1871,

completed

the

manu-

%

script

of

a

most

engaging

social

satire,

Erewhon.

Three

chapters

of

Erewhon,

originally

appearing

under

the

title

"Darwin

Among

the

Machines,"

are

a

witty

parody

of

The

Origin

of

Species.

In

the

topsy-

turvy

logic

of

satirical

writing,

Butler

sees

machines

as'

gradually

evolving

into

higher

forms.

He

considers

the

classification

of

machines

into

genera,

species

and

vari-

C.

E.

Shannon

first

became

known

for

a paper

in

which

he

applied

Boolean

Algebra

to

relay

switching

circuits;

this

laid

the

foundation

for

the

present

extensive

application

of

Boolean

Algebra

to

computer

design.

Dr.

Shannon,

who

is

engaged

in

mathematical

research

at

Bell

Telephone

Laboratories,

is

an

authority

on

information

theory.

More

recently

he

received

wide

notice

for

his

ingenious

maze-solving

mechanical

mouse,

and

he

is

well-known

as

one

of

the

leading

explorers

into

the

exciting,

but

uncharted

world

of

new

ideas

in

the

computer

field.

The

Editors

asked

Dr.

Shannon

to

write

a

paper

describing

current

experiments,

and

specula-

tions

concerning

future

developments

in

computer

logic.

Here

is

a

real

challenge

for

those

in

search

of

a

field

where

creative

ability,

imagination,

and

curiosity

will

undoubtedly

lead

to

major

advances

in

human

knowledge.-The

Editor

1234

October

Shannon:

Computers

and

Automata

eties,

their

feeding

habits,

their

rudimentary

sense

or-

gans,

their

reproductive

and

evolutionary

mechanisms

(inefficient

machines

force

men

to

design

more

efficient

ones),

tendencies

toward

reversion,

vestigial

organs,

and

even

the

problem

of

free

will

in

machines.

Rereading

Erewhon

today

one

finds

"The

Book

of

the

Machines"

disturbingly

prophetic.

Current

and

pro-

jected

computers

and

control

systems

are

indeed

as-

suming

more

and

more

the

capacities

and

functions

of

animals

and

man,

to

a

far

greater

degree,

in

fact,

than

was

envisaged

by

Butler.

The

bread-and-butter

work

of

large-scale

computers

has

been

the

solution

of

involved

numerical

problems.

To

many

of

us,

however,

the

most

exciting

potentialities

of

computers

lie

in

their

ability

to

perform

non-numer-

ical

operations-to

work

with

logic,

translate

lan-

guages,

design

circuits,

play

games,

co-ordinate

sensory

and

manipulative

devices

and,

generally,

assume

com-

plicated

functions

associated

with

the

human

brain.

Non-numerical

computation

is

by

no

means

an

un-

proven

offspring

of

the

more

publicized

arithmetic

cal-

culation.

The

shoe

is

rather

on

the

other

foot.

A

hun-

dred

years

ago

Charles

Babbage

was

inspired

in

the

design

of

his

remarkably

prescient

analytical

engine

by

a

portrait

woven

in

silk

on

a

card

controlled

Jacquard

loom-a

device

then

in

existence

half

a

century.

The

largest

and

most

reliable

current

information

processing

machine

is

still

the

automatic

telephone

system.

Our

factories

are

filled

with

ingenious

and

unsung

devices

performing

almost

incredible

feats

of

sensing,

processing

and

transporting

materials

in

all

shapes

and

forms.

Rail-

way

and

power

systems

have

elaborate

control

and

pro-

tective

networks

against

accidents

and

human

errors.

These,

however,

are

all

special-purpose

automata.

A

significant

new

concept

in

non-numerical

computation

is

the

idea

of

a

general-purpose

programmed

computer-

a

device

capable

of

carrying

out

a

long

sequence

of

elementary

orders

analogous

to

those

of

a

numerical

computer.

The

elementary

orders,

however,

will

relate

not

to

operations

on

numbers

but

to

physical

motions,

operations

with

words,

equations,

incoming

sensory

data,

or

almost

any

physical

or

conceptual

entities.

This

paper

reviews

briefly

some

of

the

research

in

non-

numerical

computation

and

discusses

certain

of

the

problems

involved.

The

field

is

currently

very

active

and

in

a

short

paper

only

a

few

sample

developments

can

be

mentioned.

THE

BRAIN

AND

COMPUTERS

The

brain

has

often

been

compared,

perhaps

over-

enthusiastically,

with

computing

machines.

It

contains

roughly

1010

active

elements

called

neurons.

Because

of

the

all

or

none

law

of

nervous

action,

neurons

bear

some

functional

resemblance

to

our

binary

computer

elements,

relays,

vacuum

tubes

or

transistors.

The

num-

ber

of

elements

is

six

orders

of

magnitude

greater

than

our

largest

computers.

McCullough

has

picturesquely

put

it

that

a

computer

with

as

many

tubes

as

a

man

has

neurons

would

require

the

Empire

State

building

to

house

it,

Niagara

Falls

to

power

it

and

the

Niagara

river

to

cool

it.

The

use

of

transistors

in

such

a

com-

parison

would

improve

the

figures

considerably,

power

requirements

coming

down

to

the

hundreds

of

kilowatt

range

(the

brain

dissipates

some

25

watts)

and

size

re-

quirements

(with

close

packing)

comparable

to

an

ordi-

nary

dwelling.

It

may

also

be

argued

that

the

increased

speed

of

electronic

components

by

a

factor

of,

say,

10'

might

be

partially

exchangeable

against

equipment

re-

quirements.

Comparisons

of

this

sort

should

be

taken

well

salted

-our

understanding

of

brain

functioning

is

still,

in

spite

of

a

great

deal

of

important

and

illuminating

research,

very

primitive.

Whether,

for

example,

the

neuron

itself

is

the

proper

level

for

a

functional

analysis

is

still

an

open

question.

The

random

structure

at

the

neural

level

in

number,

placement

and

interconnections

of

the

neu-

rons,

suggests

that

only

the

statistics

are

important

at

this

stage,

and,

consequently,

that

one

might

average

over

local

structure

and

functioning

before

constructing

a

mathematical

model.

The

similarities

between

the

brain

and

computers

have

often

been

pointed

out.

The

differences

are

per-

haps

more

illuminating,

for

they

may

suggest

the

im-

portant

features

missing

from

our

best

current

brain

models.

Among

the

most

important

of

these

are:

1.

Differences

in

size.

Six

orders

of

magnitude

in

the

number

of

components

takes

us

so

far

from

our

ordinary

experience

as

to

make

extrapolation

of

function

next

to

meaningless.

2.

Differences

in

structural

organization.

The

appar-

ently

random

local

structure

of

nerve

networks

is

vastly

different

from

the

precise

wiring

of

artificial

automata,

where

a

single

wrong

connection

may

cause

malfunctioning.

The

brain

somehow

is

de-

signed

so

that

overall

functioning

does

not

depend

on

the

exact

structure

in

the

small.

3.

Differences

in

reliability

organization.

The

brain

can

operate

reliably

for

decades

without

really

seri-

ous

malfunctioning

(comparable

to

the

meaning-

less

gibberish

produced

by

a

computer

in

trouble

conditions)

even

though

the

components

are

prob-

ably

individually

no

more

reliable

than

those

used

in

computers.

4.

Differences

in

logical

organization.

The

differences

here

seem

so

great

as

to

defy

enumeration.

The

brain

is

largely

self-organizing.

It

can

adapt

to

an

enormous

variety

of

situations

tolerably

well.

It

has

remarkable

memory

classification

and

access

features,

the

ability

to

rapidly

locate

stored

data

via

numerous

"coordinate

systems."

It

can

set

up

stable

servo

systems

involving

complex

relations

between

its

sensory

inputs

and

motor

outputs,

with

great

facility.

In

contrast,

our

digital

com-

puters

look

like

idiot

savants.

For

long

chains

of

arithmetic

operations

a

digital

computer

runs

cir-

cles

around

the

best

humans.

When

we

try

to

pro-

gram

computers

for

other

activities

their

entire

organization

seems

clumsy

and

inappropriate.

1235

1953

PROCEEDINGS

OF

THE

I.R.E.

5.

Differences

in

input-output

equipment.

The

brain

is

equipped

with

beautifully

designed

input

organs,

particularly

the

ear

and

the

eye,

for

sensing

the

state

of

its

environment.

Our

best

artificial

coun-

terparts,

such

as

Shepard's

Analyzing

Reader

for

recognizing

and

transcribing

type,

and

the

"Audrey"

speech

recognition

system

which

can

recognize

the

speech

sounds

for

the

ten

digits

seem

pathetic

by

comparison.

On

the

output

end,

the

brain

controls

hundreds

of

muscles

and

glands.

The

two

arms

and

hands

have

some

sixty

inde-

pendent

degrees

of

freedom.

Compare

this

with

the

manipulative

ability

of

the

digitally

controlled

milling

machine

developed

at

M.I.T.,

which

can

move

its

work

in

but

three

co-ordinates.

Most

of

our

computers,

indeed,

have

no

significant

sensory

or

manipulative

contact

with

the

real

world

but

operate

only

in

an

abstract

environment

of

num-

bers

and

operations

on

numbers.

TURING

MACHINES

The

basic

mathematical

theory

of

digital

computers

was

developed

by

A.

M.

Turing

in

1936

in

a

classic

paper

"On

Computable

Numbers

with

an

Application

to

the

Entscheidungsproblem."

He

defined

a

class

of

computing

machines,

now

called

Turing

machines,

con-

sisting

basically

of

an

infinite

paper

tape

and

a

comput-

ing

element.

The

computing

element

has

a

finite

number

of

internal

states

and

is

capable

of

reading

from

and

writing

on

one

cell

of

the

tape

and

of

moving

it

one

cell

to

the

right

or

left.

At

a

given

time,

the

computing

ele-

ment

will

be

in

a

certain

state

and

reading

what

is

writ-

ten

in

a

particular

cell

of

the

tape.

The

next

operation

will

be

determined

by

the

current

state

and

the

symbol

being

read.

This

operation

will

consist

of

assuming

a

new

state

and

either

writing

a

new

symbol

(in

place

of

the

one

currently

read)

or

moving

to

the

right

or

to

the

left.

It

is

possible

for

machines

of

this

type

to

compute

numbers

by

setting

up

a

suitable

code

for

interpreting

the

symbols.

For

example,

in

Turing's

formulation

the

machines

print

final

answers

in

binary

notation

on

al-

ternate

cells

of

the

tape,

using

the

other

cells

for

inter-

mediate

calculations.

It

can

be

shown

that

such

machines

form

an

ex-

tremely

broad

class

of

computers.

All

ordinary

digital

computers

which

do

not

contain

a

random

or

probabil-

istic

element

are

equivalent

to

some

Turing

machine.

Any

number

that

can

be

computed

on

these

machines,

or

in

fact

by

any

ordinary

computing

process,

can

be

computed

by

a

suitable

Turing

machine.

There

are,

however,

as

Turing

showed,

certain

problems

that

can-

not

be

solved

and

certain

numbers

that

cannot

be

com-

puted

by

any

Turing

machine.

For

example,

it

is

not

possible

to

construct

a

Turing

machine

which,

given

a

suitably

coded

description

of

another

Turing

machine,

can

always

tell

whether

or

not

the

second

Turing

ma-

chine

will

continue

indefinitely

to

print

symbols

in

the

squares

corresponding

to

the

final

answer.

It

may,

at

a

certain

point

in

the

calculation,

relapse

into

an

infinite

intermediate

computation.

The

existence

of

mechan-

ically

unsolvable

problems

of

this

sort

is

of

great

interest

to

logicians.

Turing

also

developed

the

interesting

concept

of

a

universal

Turing

machine.

This

is

a

machine

with

the

property

that

if

a

suitably

coded

description

of

any

Tur-

ing

machine

is

printed

on

its

tape,

and

the

machine

started

at

a

suitable

point

and

in

a

suitable

state,

it

will

then

act

like

the

machine

described,

that

is,

compute

(normally

at

a

much

slower

rate)

the

same

number

that

the

described

machine

would

compute.

Turing

showed

that

such

universal

machines

can

be

designed.

They

of

course

are

capable

of

computing

any

computable

num-

ber.

Most

digital

computers,

provided

they

have

ac-

cess

to

an

unlimited

memory

of

some

sort,

are

equiva-

lent

to

universal

Turing

machines

and

can,

in

principle,

imitate

any

other

computing

machine

and

compute

any

computable

number.

The

work

of

Turing

has

been

generalized

and

reformu-

lated

in

various

ways.

One

interesting

generalization

is

the

notion

of

A

computability.

This

relates

to

a

class

of

Turing

type

machines

which

have

the

further

feature

that

they

can,

at

certain

points

of

the

calculation,

ask

questions

of

a

second

"oracular"

device,

and

use

the

answers

in

further

calculations.

The

oracular

machine

may

for

example

have

answers

to

some

of

the

unsolvable

problems

of

ordinary

Turing

machines,

and

conse-

quently

enable

the

solution

of

a

larger

class

of

problems.

LOGIC

MACHINES

Boolean

algebra

can

be

used

as

a

mathematical

tool

for

studying

the

properties

of

relay

and

switching

cir-

cuits.

Conversely,

it

is

possible

to

solve

problems

of

Boolean

algebra

and

formal

logic

by

means

of

simple

relay

circuits.

This

possibility

has

been

exploited

in

a

number

of

logic

machlines.

A

typical

machine

of

this

kind,

described

by

McCallum

and

Smith,

can

handle

logical

relations

involving

up

to

seven

classes

or

truth

variables.

The

required

relations

among

these

variables,

given

by

the

logical

problem

at

hand,

are

plugged

into

the

machine

by

means

of

a

number

of

"connective

boxes."

These

connective

boxes

are

of

six

types

and

provide

for

the

logical

connectives

"not,"

"and,"

"or,"

"'or

else,"

"if

and

only

if,"

and

"if-then."

When

the

con-

nections

are

complete,

starting

the

machine

causes

it

to

hunt

through

the

27

=

128

combinaticns

of

the

basic

variables,

stopping

at

all

combinations

which

satisfy

the

constraints.

The

machine

also

indicates

the

number

of

"true"

variables

in

each

of

these

states.

McCallum

and

Smith

give

the

following

typical

problem

that

may

be

solved

on

the

machine:

It

is

known

that

salesmen

always

tell

the

truth

and

engi-

neers

always

tell

lies.

G

and

E

are

salesmen.

C

states

that

D

is

an

engineer.

A

declares

that

B

affirms

that

C

asserts

that

D

says

that

E

insists

that

F

denies

that

G

is

a

sales-

man.

If

A

is

an

engineer,

how

many

engineers

are

there?

A

very

suggestive

feature

in

this

machine

is

a

selec-

1236

October

Shannon:

Computers

and

Automata

tive

feedback

system

for

hunting

for

particular

solutions

of

the

logical

equations

without

an

exhaustive

search

through

all

possible

combinations.

This

is

achieved

by

elements

which

sense

whether

or

not

a

particular

logi-

cal

relation

is

satisfied.

If

not,

the

truth

variables

in-

volved

in

this

relation

are

caused

to

oscillate

between

their

two

possible

values.

Thus,

variables

appearing

in

unsatisfied

relations

are

continually

changing,

while

those

appearing

only

in

satisfied

relations

do

not

change.

If

ever

all

relations

are

simultaneously

satisfied

the

machine

stops

at

that

particular

solution.

Changing

only

the

variables

in

unsatisfied

relations

tends,

in

a

general

way,

to

lead

to

a

solution

more

rapidly

than

methodical

exhaustion

of

all

cases,

but,

as

is

usually

the

case

when

feedback

is

introduced,

leads

to

the

pos-

sibility

of

continual

oscillation.

McCallum

and

Smith

point

out

the

desirability

of

making

the

changes

of

the

variables

due

to

the

feedback

unbalance

as

random

as

possible,

to

enable

the

machine

to

escape

from

periodic

paths

through

various

states

of

the

relays.

GAME

PLAYING

MACHINES

The

problem

of

designing

game-playing

machines

is

fascinating

and

has

received

a

good

deal

of

attention.

The

rules

of

a

game

provide

a

sharply

limited

environ-

ment

in

which

a

machine

may

operate,

with

a

clearly

defined

goal

for

its

activities.

The

discrete

nature

of

most

games

matches

well

the

digital

computing

tech-

niques

available

without

the

cumbersome

analog-digital

conversion

necessary

in

translating

our

physical

en-

vironment

in

the

case

of

manipulating

and

sensing

machines.

Game

playing

machines

may

be

roughly

classified

into

types

in

order

of

increasing

sophistication:

1.

Dictionary-type

machines.

Here

the

proper

move

of

the

machine

is

decided

in

advance

for

each

pos-

sible

situation

that

may

arise

in

the

game

and

listed

in'

a

"dictionary"

or

function

table.

When

a

particular

position

arises,

the

machine

merely

looks

up

the

move

in

the

dictionary.

Because

of

the

extravagant

memory

requirements,

this

rather

uninteresting

method

is

only

feasible

for

excep-

tionally

simple

games,

e.g.,

tic-tac-toe.

2.

Machines

using

rigorously

correct

playing

for-

mulas.

In

some

games,

such

as

Nim,

a

complete

mathematical

theory

is

known,

whereby

it

is

pos-

sible

to

compute

by

a

relatively

simple

formula,

in

any

position

that

can

be

won,

a

suitable

winning

move.

A

mechanization

of

this

formula

provides

a

perfect

game

player

for

such

games.

3.

Machines

applying

general

principles

of

approx-

imate

validity.

In

most

games

of

interest

to

hu-

mans,

no

simple

exact

solution

is

known,

but

there

are

various

general

principles

of

play

which

hold

in

the

majority

of

positions.

This

is

true

of

such

games

as

checkers,

chess,

bridge,

poker

and

the

like.

Machines

may

be

designed

applying

such

general

principles

to

the

position

at

hand.

Since

the

principles

are

not

infallible,

neither

are

the

machines,

as

indeed,

neither

are

humans.

4.

Learning

machines.

Here

the

machine

is

given

only

the

rules

of

the

game

and

perhaps

an

elementary

strategy

of

play,

together

with

some

method

of

improving

this

strategy

through

experience.

Among

the

many

methods

that

have

been

sug-

gested

for

incorporation

of

learning

we

have:

a)

trial-and-error

with

retention

of

successful

and

elimination

of

unsuccessful

possibilities;

b)

imitation

of

a

more

successful

opponent;

c)

"teaching"

by

approval

or

disapproval,

or

by

informing

the

machine

of

the

nature

of

its

mis-

takes;

and

finally

d)

self-analysis

by

the

machine

of

its

mistakes

in

an

attempt

to

devise

general

principles.

Many

examples

of

the

first

two

types

have

been

con-

structed

and

a

few

of

the

third.

The

fourth

type,

learn-

ing

game-players,

is

reminiscent

of

Mark

Twain's

com-

ment

on

the

weather.

Here

is

a

real

challenge

for

the

programmer

and

machine

designer.

Two

exanmples

of

the

third

category,

machines

ap-

plying

general

principles,

may

be

of

interest.

The

first

of

these

is

a

machine

designed

by

E.

F.

Moore

and

the

writer

for

playing

a

commercial

board

game

known

as

Hex.

This

game

is

played

on

a

board

laid

out

in

a

regular

hexagon

pattern,

the

two

players

alternately

placing

black

and

white

pieces

in

unoccupied

hexagons.

The

entire

board

forms

a

rhombus

and

Black's

goal

is

to

connect

the

top

and

bottom

of

this

rhombus

with

a

continuous

chain

of

black

pieces.

White's

goal

is

to

con-

nect

the

two

sides

of

the

rhombus

with

a

chain

of

white

pieces.

After

a

study

of

this

game,

it

was

conjectured

that

a

reasonably

good

move

could

be

made

by

the

fol-

lowing

process.

A

two-dimensional

potential

field

is

set

up

corresponding

to

the

playing

board,

with

white

pieces

as

positive

charges

and

black

pieces

as

negative

charges.

The

top

and

bottom

of

the

board

are

negative

and

the

two

sides

positive.

The

move

to

be

made

cor-

responds

to

a

certain

specified

saddle

point

in

this

field.

To

test

this

strategy,

an

analog

device

was

constructed,

consisting

of

a

resistance

network

and

gadgetry

to

lo-

cate

the

saddle

points.

The

general

principle,

with

some

improvements

suggested

by

experience,

proved

to

be

reasonably

sound.

With

first

move,

the

machine

won

about

seventy

per

cent

of

its

games

against

human

op-

ponents.

It

frequently

surprised

its

designers

by

choos-

ing

odd-looking

moves

which,

on

analysis,

proved

sound.

We

normally

think

of

computers

as

expert

at

long

in-

volved

calculations

and

poor

in

generalized

value

judg-

ments.

Paradoxically,

the

positional

judgment

of

this

machine

was

good;

its

chief

weakness

was

in

end-game

combinatorial

play.

It

is

also

curious

that

the

Hex-player

reversed

the

usual

computing

procedure

in

that

it

solved

a

basically

digital

problem

by

an

anlog

machine.

The

game

of

checkers

has

recently

been

programmed

into

a

general-purpose

computer,

using

a

"general

prin-

ciple"

approach.

C.

S.

Strachey

used

a

method

similar

to

1953

1237

PROCEEDINGS

OF

THE

I.R.E.

one

proposed

by

the

writer

for

programming

chess-an

investigation

of

the

possible

variations

for

a

few

moves

and

a

minimax

evaluation

applied

to

the

resulting

posi-

tions.

The

following

is

a

sample

game

played

by

the

checker

program

with

notes

by

Strachey.

(The

white

squares

are

numbered

consecutively,

0-31,

from

left

to

right

and

top

to

bottom.

Numbers

in

parentheses

indi-

cate

captures.)

MACHINE

STRACHEY

11-15

23-18

7-11

21-17

8-12

20-16

a

12-21

(16)

25-16

(21)

9-14

!

b

18-

9

(14)

6-20

(16,

9)

c

27-23

2-

7

d

23-18

5-

8

18-14

8-13

e

17-

8

(13)

4-13

(8)

14-

9

1-Sf

9-

6

15-19

6-

1

(K)

5-9

1-6?g

0-

5

1

h

6-15

(10)

11-25

(22,

15)

30-21

(25)

13-17

21-14

(17)

9-18

(14)

24-21

18-23

26-22

23-27

22-17

5-8

i

17-14

8-13

14-

9

19-23

9-

6

23-26

j

31-22

(26)

27-31

(K)

6-

2

(K)

7-10

2-

7

10-15

21-16

?k

3-10

(7)

16-

9

(13)

10-14

9-

6

15-19

6-

2

(K)

31-27

m

2-

6

27-31

m

6-10

31-26

n

10-17

(14)

19-23

29-25

26-31

p

Notes:

a)

An

experiment

on

my

part-the

only

deliberate

offer

I

made.

I

thought,

wrongly,

that

it

was

quite

safe.

b)

Not

foreseen

by

me.

c)

Better

than

5-21

(9,

17).

d)

A

random

move

(zero

value).

Shows

the

lack

of

a

constructive

plan.

e)

Another

random

move

of

zero

value.

Actually

rather

good.

f)

Bad.

Ultimately

allows

me

to

make

a

King.

10-14

would

would

have

been

better.

g)

A

bad

slip

on

my

part.

h)

Taking

full

advantage

of

my

slip.

i)

Bad,

unblocks

the

way

to

a

King.

j)

Sacrifice

in

order

to

get

a

King

(not

to

stop

me

Kinging).

A

good

move,

but

not

possible

before

19-23

had

been

made

by

chance.

k)

Another

bad

slip

on

my

part.

m)

Purposeless.

The

strategy

is

failing

badly

in

the

end

game.

n)

Too

late.

p)

Futile.

The

game

was

stopped

at

this

point

as

the

outcome

was

obvious.

While

obviously

no

world

champion,

the

machine

is

certainly

better

than

many

humans.

Strachey

points

out

various

weaknesses

in

the

program,

particularly

in

certain

end-game

positions,

and

suggests

possible

im-

provements.

LEARNING

MACHINES

The

concept

of

learning,

like

those

of

thinking,

con-

sciousness

and

other

psychological

terms,

is

difficult

to

define

precisely

in

a

way

acceptable

to

the

various

inter-

ested

parties.

A

rough

formulation

might

be

framed

somewhat

as

follows.

Suppose

that

an

organism

or

a

ma-

chine

can

be

placed

in,

or

connected

to,

a

class

of

en-

vironments,

and

that

there

is

a

measure

of

"success"

or

"adaptation"

to

the

environment.

Suppose

further

that

this

measure

is

comparatively

local

in

time,

that

is,

that

one

can

measure

the

success

over

periods

of

time

short

compared

to

the

life

of

the

organism.

If

this

local

meas-

ure

of

success

tends

to

improve

with

the

passage

of

time,

for

the

class

of

environments

in

question,

we

may

say

that

the

organism

or

machine

is

learning

to

adapt

to

these

environments

relative

to

the

measure

of

success

chosen.

Learning

achieves

a

quantitative

significance

in

terms

of

the

broadness

and

complexity

of

the

class

of

environments

to

which

the

machine

can

adapt.

A

chess

playing

machine

whose

frequency

of

wins

increases

dur-

ing

its

operating

life

may

be

said

by

this

definition

to

be

learning

chess,

the

class

of

environments

being

the

chess

players

who

oppose

it,

and

the

adaptation

meas-

sure,

the

winning

of

games.

A

number

of

attempts

have

been

made

to

construct

simple

learning

machines.

The

writer

constructed

a

maze-solving

device

in

which

an

arbitrary

maze

can

be

set

up

in

a

five-by-five

array

of

squares,

by

placing

partitions

as

desired

between

adjacent

squares.

A

per-

manently

magnetized

"mouse,"

placed

in

the

maze,

blunders

about

by

a

trial

and

error

procedure,

striking

various

partitions

and

entering

blind

alleys

until

it

eventually

finds

its

way

to

the

"food

box."

Placed

in

the

maze

a

second

time,

it

will

move

directly

to

the

food

box

from

any

part

of

the

maze

that

it

has

visited

in

its

first

exploration,

without

errors

or

false

moves.

Placed

in

other

parts

of

the

maze,

it

will

blunder

about

until

it

reaches

a

previously

explored

part

and

from

there

go

directly

to

the

goal.

Meanwhile

it

will

have

added

the

information

about

this

part

of

the

maze

to

its

memory,

and

if

placed

at

the

same

point

again

will

go

directly

to

the

goal.

Thus

by

placing

it

in

the

various

unexplored

parts

of

the

maze,

it

eventually

builds

up

a

complete

pattern

of

information

and

is

able

to

reach

the

goal

di-

rectly

from

any

point.

If

the

maze

is

now

changed,

the

mouse

first

tries

the

old

path,

but

on

striking

a

partition

starts

trying

other

directions

and

revising

its

memory

until

it

eventually

reaches

the

goal

by

some

other

path.

Thus

it

is

able

to

forget

an

old

solution

when

the

problem

is

changed.

The

mouse

is

actually

driven

by

an

electromagnet

moving

beneath

the

maze.

The

motion

of

the

electro-

magnet

is

controlled

by

a

relay

circuit

containing

about

110

relays,

organized

into

a

memory

and

a

computing

circuit,

somewhat

after

that

of

a

digital

computer.

The

maze-solver

may

be

said

to

exhibit

at

a

very

primitive

level

the

abilities

to

(1)

solve

problems

by

trial

and

error,

(2)

repeat

the

solutions

without

the

errors,

(3)

add

and

correlate

new

information to

a

par-

tial

solution,

(4)

forget

a

solution

when

it

is

no

longer

applicable.

1238

October

Shannon:

Computers

and

Automata

Another

approach

to

mechanized

learning

is

that

of

saitably

programming

a

large-scale

computer.

A.

E.

Oettinger

has

developed

two

learning

programs

for

the

Edsac

computer

in

Cambridge,

England.

In

the

first

of

these,

the

machine

was

divided

into

two

parts,

one

part

playing

the

role

of

a

learning

machine

and

the

second

its

environment.

The

environment

represented

ab-

stractly

a

number

of

stores

in

which

various

items

might

be

purchased,

different

stores

stocking

different

classes

of

items.

The

learning

machine

faced

the

problem

of

learning

where

various

items

might

be

purchased.

Start-

ing

off

with

no

previous

knowledge

and

a

particular

item

to

be

obtained,

it

would

search

at

random

among

the

stores

until

the

item

was

located.

When

finally

suc-

cessful,

it

noted

in

its

memory

where

the

article

was

found.

Sent

again

for

the

same

article

it

will

go

directly

to

the

shop

where

it

previously

obtained

this

article.

A

further

feature

of

the

program

was

the

introduction

of

a

bit

of

"curiosity"

in

the

learning

machine.

When

it

succeeded

in

finding

article

number

j

in

a

particular

shop

it

also

noticed

whether

or

not

that

shop

carried

articles

j-

1

and

j+

1

and

recorded

these

facts

in

its

memory.

The

second

learning

program

described

by

Oettinger

is

modeled

more

closely

on

the

conditioned

reflex

be-

havior

of

animals.

A

stimulus

of

variable

intensity

can

be

applied

to

the

machine

in

the

form

of

an

input

in-

teger.

To

this

stimulus

the

machine

may

respond

in

a

number

of

different

ways

indicated

by

an

output

in-

teger.

After

the

response,

it is

possible

for

the

operator

to

indicate

approval

or

disapproval

by

introducing

a

third

integer

at

a

suitable

point.

When

the

machine

starts

operating,

its

responses

to

stimuli

are

chosen

at

random.

Indication

of

approval

improves

the

chances

for

the

response

immediately

preceding;

indication

of

dis-

approval

reduces

this

chance.

Furthermore,

as

a

par-

ticular

response

is

learned

by

conditioning

it

with

ap-

proval,

the

stimulus

required

for

this

response

decreases.

Finally,

there

is

a

regular

decay

of

thresholds

when

no

approval

follows

a

response.

Further

embellishments

of

programs

of

this

sort

are

limited

only

by

the

capacity

of

the

computer

and

the

energy

and

ingenuity

of

the-

program

designer.

Unfor-

tunely,

the

elementary

orders

available

in

most

large-

scale

computers

are

poorly

adapted

to

the

logical

re-

quirements

of

learning

programs,

and

the

machines

are

therefore

used

rather

inefficiently.

It

may

take

a

dozen

or

more

orders

to

represent

a

logically

simple

and

fre-

quently

used

operation

occurring

in

a

learning

routine.

Another

type

of

learning

machine

has

been

con-

structed

by

D.

W.

Hagelbarger.

This

is

a

machine

de-

signed

to

play

the

game

of

matching

pennies

against

a

human

opponent.

On

the

front

panel

of

the

machine

are

a

start

button,

two

lights

marked

+

and

-,

and

a

key

switch

whose

extreme

positions

are

also

marked

+

and

-.

To

play

against

the

machine,

the

player

chooses

+

or

-,

and

then

pushes

the

start

button.

The

machine

will

then

light

up

one

of

the

two

lights.

If

the

machine

matches

the

player,

that

is,

lights

the

light

correspond-

ing

to

the

choice

of

the

player,

the

machine

wins;

other-

wise

the

player

wins.

When

the

play

is

complete,

the

player

registers

by

appropriate

movement

of

the

key

switch

the

choice

he

made.

The

machine

is

so

constructed

as

to

analyze

certain

patterns

in

the

players'

sequence

of

choices,

and

at-

tempt

to

capitalize

on

these

patterns

when

it

finds

them.

For

example,

some

players

have

a

tendency

if

they

have

won

a

round,

played

the

same

thing

and

won

again,

to

then

change

their

choice.

The

machine

keeps

count

of

these

situations

and,

if

such

tendencies

appear,

plays

in

such

a

way

as

to

win.

When

such

patterns

do

not

ap-

pear

the

machine

plays

at

random.

It

has

been

found

the

machine

wins

about

55-60

per

cent

of

the

rounds,

while

by

chance

or

against

an

op-

ponent

that

played

strictly

at

random

it

would

win

only

50

per

cent

of

the

time.

It

appears

to

be

quite

difficult

for

a

human

being

to

produce

a

random

sequence

of

pluses

and

minuses

(to

insure

the

50

per

cent

wins

he

is

entitled

to

by

the

theory

of

games)

and

even

more

difficult

to

actually

beat

the

machine

by

leading

it

on

to

suspect

patterns,

and

then

re-versing

the

patterns.

A

second

penny-matching

machine

was

designed

by

the

writer,

following

the

same

general

strategy

but

using

a

different

criterion

to

decide

when

to

play

at

random

and

when

to

assume

that

an

apparent

behavior

pattern

is

significant.

After

considerable

discussion

as

to

which

of

these

two

machines

could

beat

the

other,

and

fruitless

attempts

to

solve

mathematically

the

very

complicated

statistical

problem

involved

when

they

are

connected

together,

the

problem

was

relegated

to

experiment.

A

third

small

machine

was

constructed

to

act

as

umpire

and

pass

the

information

back

and

forth

between

the

machines

concerning

their

readiness

to

make

a

move

and

the

choices

made.

The

three

machines

were

then

plugged

together

and

allowed

to

run

for

a

few

hours,

to

the

ac-

companiment

of

small

side-bets

and

loud

cheering.

Ironically,

it

turned

out

that

the

smaller,

more

precipi-

tate

of

the

two

machines

consistently

beat

the

larger,

more

deliberate

one

in

a

ratio

of

about

55

to

45.

A

still

different

type

of

learning

machine

was

devised

by

W.

Ross

Ashby

who

christened

it

the

Homeostat.

Homeostasis,

a

word

coined

by

Walter

B.

Cannon,

re-

lates

to

an

animal's

ability

to

stabilize,

by

feedback,

such

biological

variables

as

body

temperature,

chemical

concentrations

in

the

blood

stream,

etc.

Ashby's

device

is

a

kind

of

self-stabilizing

servo

system.

The

first

model

of

the

Homeostat

contained

four

interconnected

servos.

The

cross-connections

of

these

servos

passed

through

four

stepping

switches

and

resistors

connected

to

the

points

of

the

steppers.

Thus

the

effect

of

unbalance

in

the

other

three

loops

on

a

particular

loop

depended

on

the

values

of

the

resistors

being

contacted

by

the

stepper

associated

with

that

loop.

When

any

one

of

the

servos

was

sufficiently

out

of

balance,

a

corresponding

limit

relay

would

operate

and

cause

the

corresponding

step-

ping

switch

to

advance

one

point.

Now

normally,

a

1953

1239

PROCEEDINGS

OF

THE

I.R.E.

servo

system

with

four

degrees

of

freedom

and

random

cross-

and

self-gain

figures

will

not

be

stable.

If

this

occurred,

one

or

more

of

the

stepping

switches

would

advance

and

a

new

set

of

resistors

would

produce

a

new

set

of

gain

figures.

If

this

set

again

proved

unstable,

a

further

advance

of

the

steppers

would

occur

until

a

stable

situation

was

found.

The

values

of

the

resistors

connected

to

the

stepping

switches

were

chosen

by

ran-

dom

means

(using

a

table

of

randon

numbers).

Facilities

were

provided

for

introducing

many

arbitrary

changes

or

constraints

among

the

servos.

For

example,

their

con-

nections

could

be

reversed,

two

of

them

could

be

tied

together,

one

of

them

held

at

a

fixed

value,

etc.

Under

all

these

conditions,

the

mechanism

was

able

to

find

a

suitable

stable

position

with

all

the servos

in

balance.

Considering

the

machine's

goal

to

be

that

of

stabilizing

the

servos,

and

the

environment

to

be

represented

by

the

various

alterations

and

constraints

introduced

by

the

operator,

the

Homeostat

may

be

said

to

adapt

to

its

environment.

Certain

features

of

the

Homeostat

are

quite

attrac-

tive

as

a

basis

for

learning

machines

and

brain

models.

It

seems

in

certain

ways

to

do

a

bit

more

than

was

ex-

plicitly

designed

into

it.

For

example,

it

has

been

able

to

stabilize

under

situations

not

anticipated

when

the

machine

was

constructed.

The

use

of

randomly

chosen

resistors

is

particularly

suggestive

and

reminiscent

of

the

random

connections

among

neurons

in

the

brain.

Ashby,

in

fact,

believes

that

the

general

principle

em-

bodied

in

the

Homeostat,

which

he

calls

ultra-stability,

may

underlie

the

operation

of

the

animal

nervous

sys-

tem.

One

of

the

difficulties

of

a

too

direct

application

of

this

theory

is

that,

as

Ashby

points

out,

the

time

required

for

finding

a

stable

solution

grows

more

or

less

exponentially

with

the

number

of

degrees

of

free-

dom.

With

only

about

20

degrees

of

freedom,

it

would

require

many

lifetimes

to

stabilize

one

system.

At-

tempts

to

overcome

this

difficulty

lead

to

rather

in-

volved

conceptual

constructions,

so

involved

that

it

is

extremely

difficult

to

decide

just

how

effectively

they

would

operate.

Our

mathematical

tools

do

not

seem

sufficiently

sharp

to

solve

these

problems

and

further

experimental

work

would

be

highly

desirable.

SELF-REPRODUCING

MACHINES

In

Erewhon

the

reproduction

process

in

machines

was

pictured

as

a

kind

of

symbiotic

co-operation

between

man

and

machines,

the

machines

using

man

as

an

inter-

mediary

to

produce

new

machines

when

the

older

ones

were

worn

out.

Man's

part

is

akin

to

that

of

the

bee

in

the

fertilization

of

flowers.

Recently

von

Neumann

has

studied

at

an

abstract

level

the

problem

of

true

self-

reproduction

in

machines,

and

has

formulated

two

dif-

ferent

mathematical

models

of

such

"machines."

The

first

of

these

may

be

pictured

somewhat

as

fol-

lows.

"Machines"

in

the

model

are

constructed

from

a

small

number

(of

the

order

of

twenty)

types

of

ele-

mentary

components.

These

components

have

relatively

simple

functions,

for

example,

girders

Tor

structural

pur-

poses,

elementary

logical

elements

similar

to

simplified

relays

or

neurons

for

computing,

sensing

components

for

detecting

the

presence

of

other

elements,

joining

components

(analogous

to

a

soldering

iron)

for

fastening

elements

together,

and

so

on.

From

these

elements,

vari-

ous

types

of

machines

may

be

"constructed."

In

particu-

lar,

it

is

possible

to

design

a

kind

of

universal

construc-

tion

machine,

analogous

to

Turing's

universal

comput-

ing

machine.

The

universal

constructing

machine

can

be

fed

a

sequence

of

instructions,

similar

to

the

program

of

a

digital

computer,

which

describe

in

a

suitable

code

how

to

construct

any

other

machine

that

can

be

built

with

the

elementary

components.

The

universal

con-

structing

machine

will

then

proceed

to

hunt

for

the

needed

components

in

its

environment

and

build

the

machine

described

on

its

tape.

If

the

instructions

to

the

universal

constructing

machine

are

a

description

of

the

universal

constructing

machine

itself,

it

will

proceed

to

build

a

copy

of

itself,

and

would

be

a

self-reproducing

machine

except

for

the

fact

that

the

copy

is

not

yet

supplied

with

a

set

of

instructions.

By

adding

to

the

uni-

versal

machine

what

amounts

to

a

tape-copying

device

and

a

relatively

simple

controlling

device,

a

true

self-

reproducing

machine

is

obtained.

The

instructions

now

describe

the

original

universal

machine

with

the

addi-

tion

of

the

tape

reproducer

and

the

controlling

device.

The

first

operation

of

the

machine

is

to

reproduce

this

entity.

The

controlling

device

then

sends

the

instruction

tape

through

the

tape

reproducer

to

obtain

a

copy,

and

places

this

copy

in

the

second

machine.

Finally,

it

turns

the

second

machine

on,

which

starts

reading

its

instructions

and

building

a

third

copy,

and

so

ad

in-

finitum.

More

recently,

von

Neumann

has

turned

from

this

somewhat

mechanical

model

to

a

more

abstract

self-

reproducing

structure-one

based

on

a

two-dimensional

array

of

elementary

"cells."

Each

cell

is

of

relatively

simple

internal

structure,

having,

in

fact,

something

like

thirty

possible

internal

states,

and

each

cell

communi-

cates

directly

only

with

its

four

neighbors.

The

state

of

a

cell

at

the

next

(quantized)

step

in

time

depends

only

on

the

current

state

of

the

cell

and

the

states

of

its

four

neighbors.

By

a

suitable

choice

of

these

state

transitions

it

is

possible

to

set

up

a

system

yielding

a

kind

of

self-

reproducing

structure.

A

group

of

contiguous

cells

can

act

as

an

organic

unit

and

operate

on

nearby

quiescent

cells

in

such

a

way

as

to

organize

a

group

of

them

into

an

identical

unit.

This

second

model

avoids

many

of

the

somewhat

extraneous

problems

of

locating,

recognizing

and

posi-

tioning

components

that

were

inherent

in

the

first

model,

and

consequently

leads

to

a

simpler

mathemati-

cal

formulation.

Furthermore,

it

has

certain

analogies

with

various

chemical

and

biological

problems,

such

as

those

of

crystal

and

gene

reproduction,

while

the

first

model

is

more

closely

related

to

the

problem

of

large

scale

animal

reproduction.

1240

October

Shannon:

Computers

and

Automata

An

interesting

concept

arising

from

both

models

is

the

notion

of

a

critical

complexity

required

for

self-repro-

duction.

In

either

case,

only

sufficiently

complicated

"machines"

will

be

capable

of

self-reproduction.

Von

Neumann

estimates

the

order

of

tens

of

thousands

of

components

or

cells

to

obtain

this

property.

Less

com-

plicated

structures

can

only

construct

simpler

"ma-

chines"

than

themselves,

while

more

complicated

ones

may

be

capable

of

a

kind

of

evolutionary

improvement

leading

to

still

more

complicated

organisms.

CHALLENGE

TO

THE

READER

We

hope

that

the

foregoing

sample

of

non-numerical

computers

may

have

stimulated

the

reader's

appetite

for

research

in

this

field.

The

problem

of

how

the

brain

works

and

how

machines

may

be

designed

to

simulate

its

activity

is

surely

one

of

the

most

important

and

difficult

facing

current

science.

Innumerable

questions

demand

clarification,

ranging

from

experimental

and

development

work

on

the

one

hand

to

purely

mathe-

matical

research

on

the

other.

Can

we

design

significant

machines

where

the

connections

are

locally

random?

Can

we

organize

machines

into

a

hierarchy

of

levels,

as

the

brain

appears

to

be

organized,

with

the

learning

of

the

machine

gradually

progressing

up

through

the

hier-

archy?

Can

we

program

a

digital

computer

so

that

(eventually)

99

per

cent

of

the

orders

it

follows

are

written

by

the

computer

itself,

rather

than

the

few

per

cent

in

current

programs?

Can

a

self-repairing

machine

be

built

that

will

locate

and

repair

faults

in

its

own

components

(including

components

in

the

maintenance

part

of

the

machine)?

What

does

a

random

element

add

in

generality

to

a

Turing

machine?

Can

manipulative

and

sensory

devices

functionally

comparable

to

the

hand

and

eye

be

developed

and

coordinated

with

com-

puters?

Can

either

of

von

Neumann's

self-reproducing

models

be

translated

into

hardware?

Can more

satis-

factory

theories

of

learning

be

formulated?

Can

a

ma-

chine

be

constructed

which

will

design

other

machines,

given

only

their

broad

functional

characteristics?

What

is

a

really

good

set

of

orders

in

a

digital

computer

for

general

purpose

non-numerical

computation?

How

can

a

computer

memory

be

organized

to

learn

and

remem-

ber

by

association,

in

a

manner

similar

to

the

human

brain?

We

suggest

these

typical

questions,

and

the

entire

automata

field,

as

a

challenge

to

the

reader.

Here

is

research

territory

ripe

for

scientific

prospectors.

It

is

not

a

matter

of

reworking

old

operations,

but

of

locat-

ing

the

rich

new

veins

and

perhaps

in

some

cases

merely

picking

up

the

surface

nuggets.

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C..\.5D

1953

1241